Question

Find tаn Ө. A. 15/17 B.15/8 C.8/15 D.8/17

Answer 1

$\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}$

$\tan(\theta) = \frac{perpendicular}{base}$

we can see we aren't provided with the perpendicular , so let's find it using Pythagoras Theorem !

$H {}^{2} = P {}^{2} + B {}^{2} \\ \\ \dashrightarrow 17 {}^{2} = P {}^{2} + 8 {}^{2} \\ \\ \dashrightarrow \: P {}^{2} = 17 {}^{2} - 8 {}^{2} \\ \\ \dashrightarrow \: P {}^{2} = 289 - 64 \\ \\ \dashrightarrow \: P { }^{2} = 225 \\ \\ \dashrightarrow \: P = \sqrt{225} \\ \\ \dashrightarrow \: P = 15$

substituting the value of P in the formula

$\tan(\theta) = \frac{15}{8}$

therefore , option ( B ) is correct !

hope helpful ~